Democrats from New York's Queens borough slammed Amazon's plan for offices in the area, setting up a potential political fight with one of the world's most powerful companies.

The criticism came even as Virginia lawmakers largely welcomed the e-commerce company's decision to open up another facility outside Washington, D.C.

Amazon announced plans Tuesday to split what it calls its second headquarters between Long Island City in Queens and Arlington, Virginia. The company says it will invest $5 billion and create more than 50,000 jobs in the two areas. Amazon will get more than $2 billion in what it calls "performance-based direct incentives" from state and local governments.

Local Democrats, with a few high-profile exceptions, swiftly criticized Amazon. They raised concerns about cost of living increases, a potential lack of benefit to local community members and state tax incentives going to a large corporation rather than residents. The response sets up a political clash for Amazon — a company that has had no shortage of battles with officials as it extends its reach across the country and globe.

Rick Loomis | Getty Images

Alexandria Ocasio-Cortez addresses the crowd gathered at La Boom night club in Queens on November 6, 2018 in New York City. With her win against Republican Anthony Pappas, Ocasio-Cortez became the youngest woman elected to Congress.

Democratic Representative-elect Alexandria Ocasio-Cortez, who will represent parts of Queens and the Bronx starting in January, said early Tuesday that her future constituents raised concerns about the Amazon offices. In a series of tweets, she called it "extremely concerning" that Amazon would get tax breaks "when our subway is crumbling and our communities need MORE investment, not less."

Ocasio-Cortez expressed concerns about the project pushing working-class people out of Queens. She wrote that "we need to focus on good healthcare, living wages, affordable rent" and that "corporations that offer none of those thing should be met w/skepticism."

"Lastly, this isn't just about one company or one headquarters. It's about cost of living, corps paying their fair share, etc," she wrote in another tweet. "It's not about picking a fight, either. I was elected to advocate for our community's interests - & they've requested, clearly, to voice their concerns."

Two other Democratic lawmakers who represent Queens also criticized the company. In a joint statement, state Sen. Michael Gianaris and City Council Member Jimmy Van Bramer said "it is unfathomable" that New York would offer Amazon billions of dollars in incentives when "our subways are crumbling, our children lack school seats, and too many of our neighbors lack adequate health care."

"Too much is at stake to accept this without a fight," they said. "We will continue to stand up against what can only be described as a bad deal for New York and for Long Island City."

It is unclear what action the lawmakers can or will take to modify or scrap the project. Last week, Democrats won back the New York Senate, giving the party unified control of state government and potentially increasing the chances of legislative action related to Amazon.

State Assemblyman Ron Kim, who represents parts of Queens, plans to introduce legislation to cancel the Amazon subsidies and redirect the tax breaks to student debt relief. It is unclear how much support the measure could draw.

Amazon did not immediately respond to CNBC's request for comment. Amazon's top spokesman, former White House press secretary Jay Carney, contended that the company's economic boost to New York and Virginia would make up for the tax breaks.

"We really are confident that these performance-based incentives will absolutely pay for themselves and then some for each community," Carney told CNBC's "Power Lunch" on Tuesday.

Not all New York Democrats oppose Amazon's presence in the city. In a joint news conference Tuesday, Mayor Bill de Blasio and Gov. Andrew Cuomo — who frequently butt heads — cheered Amazon's decision.

De Blasio tried to assuage concerns about harm to locals, saying "we measure success in how many everyday people benefit" from Amazon. He said that he wants to support Long Island City's growth "with the kind of infrastructure investment needed."

Cuomo said that Amazon's move "is a big money maker for us" in order to reinvest money in the subway system and education. He added that "we had to win the competition" to get the company to open offices, which included the tax incentive package.

Former Mayor Michael Bloomberg, a potential Democratic presidential candidate in 2020, also cheered the decision, saying it vindicates the city's efforts to become a technology hub.

The reactions to Amazon highlight a gulf between the more mainstream, pro-business wing of the Democratic Party and its more anti-establishment officials. The party's left wing has taken aim at various corporations and executives, such as Amazon and billionaire CEO Jeff Bezos, who they say have taken advantage of workers.

In October, Amazon increased its hourly minimum wage for all U.S. employees to $15 per hour. While it is unclear how much he directly influenced the decision, leftist Sen. Bernie Sanders, a Vermont independent, had repeatedly hammered Amazon and Bezos over their treatment of workers.

The divide in the Democratic Party was further highlighted in the reactions of top Virginia Democrats. Sen. Mark Warner, D-Va., said he was "excited about the potential" Amazon offers but added that "we must commit to implementing this announcement in a way that will benefit the whole region" and all of Virginia.